If a giant star in a binary overfills its Roche lobe, the giant's
convective envelope may respond by expanding faster than its Roche lobe,
transferring mass on a dynamical time scale, and creating a common
envelope (CE) that engulfs both stars. Orbital energy may then be
transferred from the binary to the envelope, which can shrink the orbit
and drive away the material, leaving behind a detached system containing
the white dwarf core of the giant. Such a CE event is thought to be
critical for explaining certain populations of exotic stars (e.g.,
cataclysmic variables). Yet the application of CE evolution to binary
population synthesis and N-body or Monte Carlo star cluster models
requires many poorly constrained assumptions, which may lead to
unphysical evolutionary paths. In fact, we find that such fictitious
systems are created regularly within our N-body models of the old (7
Gyr) open cluster NGC 188. Most notably, the model predicts a population
of post-CE long-period ( 1000 days) circular solar-type main sequence -
white dwarf binaries, that are not present in our observations of the
true binaries in NGC 188, or any other solar-type binary population in
the literature (in star clusters or in the field). The absence of such
post-CE systems in real binary populations places important limits on
parameters used in most models of CE evolution, and may suggest that
more binaries undergo stable mass transfer than has previously been
assumed. We discuss how various solutions to this problem would impact
other observable stellar populations, including cataclysmic variables,
symbiotic stars and blue stragglers.